Respuesta :
Answer:
b. decrease the width of the confidence interval
True. For this case the width is given by:
[tex] Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease
Step-by-step explanation:
If all other factors are held constant, increasing the sample size will
We can analyze the situation one by one
a. increase the estimated standard error
For this case the standard error is given by:
[tex] SE = \frac{\sigma}{\sqrt{n}}[/tex]
False, we can't increase the standard error, increasing the denominator.
b. decrease the width of the confidence interval
True. For this case the width is given by:
[tex] Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease
c. increase the width of the confidence interval
False. For this case the width is given by:
[tex] Width = 2 ME= 2 z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
And if we see since we are increasing the sample size (value of n) then the margin of error would be lower and then the width of the interval will decrease and not increase
d. none of the above
False. Option c is correct.
